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lfunc_lfunctions • Show schema
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{'Lhash': '2914042537864737740078400497566', 'a10': [4.826982565855492, -1.1235652762035362e-60], 'a2': [2.848331387439776, 0.9254789691775847], 'a3': [0.0, 0.0], 'a4': [4.020412392784806, 2.9210005834779547], 'a5': [1.5328436732625097, -0.49805110068898695], 'a6': [0.0, 0.0], 'a7': [2.69387665817807, 1.9572159573673285], 'a8': [1.7066797652128076, 2.3490431728728955], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.6975546171669396, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [9.456704187028905, -5.618785092796305]]]], 'bad_primes': [3, 11], 'central_character': '99.53', 'coefficient_field': 'CDF', 'conductor': 99, 'conductor_radical': 33, 'conjugate': '3391598733539818930620128666453', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.848331387439776, -0.9254789691775847], [3.23606797749979, 2.3511410091698925]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.5328436732625097, 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'data': '3.86756239510039142207402562470', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.12567435108905550924913210505', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.6975546171669396, 'bad_primes': [3, 11], 'central_character': '33.20', 'conductor': 99, 'conductor_radical': 33, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/99/3/l/a/53/7'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-99-33.20-c2-0-4', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-99-33.20-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6424233976557139, 'root_angle': -0.09056462383944819, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '2.29877423427251158356596287454', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2914042537864737740078400497566', 'Lhash_array': ['2914042537864737740078400497566'], 'label': '2-99-33.20-c2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/99/3/l/a/53/7'}